Question

The density of wool is 0.65 g $c{{m}^{-3}}$ in CGS System. Its Density in SI System is,
A.) \[65kg{{m}^{-3}}\]
B.) $6.5kg{{m}^{-3}}$
C.) $650kg{{m}^{-3}}$
D.) $0.65kg{{m}^{-3}}$

Answer 1

Hint: The centimeter gram seconds (CGS) and the meters kilogram seconds (SI) unit systems. These two are the unit systems for measurement of quantities. Most of the time we use the SI unit system but sometimes in our question we are given a CGS system and hence we need to convert it into an SI system.

Complete Step by Step Solution:
To convert CGs into SI unit system, first we need to know about the basic conversion factors such as
1 metre = 100 centimetres
1 Kilogram = 1000 grams
${{1}^{0}}C$= ${{273}^{0}}Kelvin$
1 minute = 60 seconds

Now for the above question we are given a quantity in grams (CGS Unit System) and centimeters and we need to convert it into kilograms and meters (SI Unit system).

To convert grams into kilograms first we need to divide it by 1000 because 1 Kilogram = 1000 grams

So, we are given with 0.65 g $c{{m}^{3}}$and by dividing it by 1000 we get,
\[\dfrac{0.65\text{ }g~c{{m}^{-3}}}{1000}\]
$0.00065kgc{{m}^{-3}}$
To convert $c{{m}^{3}}$into ${{m}^{3}}$we need to multiply it by 1000000

So, we have $0.00065kgc{{m}^{-3}}$
$0.00065kgc{{m}^{-3}}\times 1000000$
We get $650kg{{m}^{-3}}$

Hence, our option C is the correct answer.

Additional Information:
In many fields of science and engineering, the SI unit system is used. However, there are certain subjects where CGS is still used. For example, in electrodynamics and electromagnetism the CGS or Gaussian units are still used as the equations seems simpler and easy to solve as compared to those in SI system

Note:
Always make sure that you use the same system for the answer as given or asked in the system. When converting to the other unit make sure that you re check your calculations as almost all the mistakes in these types of questions are due to the wrong calculations. So always re check your calculations while doing unit conversion